The time, at an average speed of 251.882kph, was more than two seconds quicker than the previous record of 3:16.887 set by Switzerland's Neel Jani for Porsche in 2015 qualifying.
It was also faster than German driver Hans Stuck's 1985 pole of 3:14.800 set on a shorter track with fewer corners.
Kobayashi had already put Toyota on provisional pole on Wednesday after lapping in 3:18.793 in the opening night session.
"Mike Conway told me the car was perfect, so I set off fully confident ... I had 100 percent confidence in the car and when you're in that frame of mind, you can do great things," said Kobayashi.
"It was an incredible lap, the car was amazing, and we went after it without any trouble whatsoever with traffic. It surpassed all our hopes. It's rare to be able to say this, but it was a perfect lap.
"When I saw the time as I crossed the line, I said to myself, wow!"
Only one Japanese manufacturer has won Le Mans, Mazda in 1991, and Toyota -- five times runners up -- have made winning the world's greatest sportscar race their main motorsport target after losing to Porsche for the past two years.
The number eight Toyota, driven by Britain's Anthony Davidson, Japan's Kazuki Nakajima and Switzerland's Sebastien Buemi, qualified second in a time of 3:17.128 with Nakajima at the wheel.
In an endurance race where pace is nothing without reliability, qualifying is more about bragging rights ahead of a gruelling weekend.
Champions Porsche filled the second row, with Jani the fastest of their drivers in the number one 919 hybrid car he shares with Germany's Andre Lotterer and Britain's Nick Tandy.
The German carmaker won last year's race after Toyota had victory snatched from their grasp by a last lap power failure just as Nakajima had seemed destined to take the chequered flag in front of 263,000 spectators.
The 85th edition of the race starts on Saturday.
(Reporting by Alan Baldwin in London, editing by Nick Mulvenney)
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